Light clock treating horizontal and vertical motion differently?

[Ibix]

I think it's also worth noting the existence of the so-called "one postulate" derivations of the Lorentz transforms, which only assume the principle of relativity. They do not use the light speed postulate, so cannot be said to assume anything special about any speed. They show that there are only two systems of physics that are consistent with the principle of relativity - the Galilean transforms and the Lorentz transforms but with an unknown finite invariant speed in the place of the $c$ that you get if you do use the second postulate. You would then use an experiment like Bertozzi's to show that we don't live in a Newtonian universe and that the unknown finite invariant speed is actually $c$, or observe that the invariant speed has to be $c$ for Maxwell's equations to be covariant.

Bertozzi's experiment:

 

[Dale]

Or zero-postulate derivations (not what they call themselves) that don’t assume either postulate and simply use experimental evidence instead.

 

[Ibix]

Or zero-postulate derivations (not what they call themselves) that don’t assume either postulate and simply use experimental evidence instead.

You're thinking of stuff like Poincaré's 1904 paper, which has the complete maths of SR collected from empirical study of electromagnetism without him quite realising what he'd got?

 

[Dale]

You're thinking of stuff like Poincaré's 1904 paper, which has the complete maths of SR collected from empirical study of electromagnetism without him quite realising what he'd got?

I didn’t know about that one. I was actually specifically thinking of Robertson’s paper “Postulate versus observation in the special theory of relativity”. He shows that, without assuming either of the postulates, we can infer the Lorentz transform to about 1% accuracy from just the Michelson Morley experiment, the Kennedy Thorndike experiment, and the Ives Stillwell experiment